A theoretical study of the highest bound states and some of the lowest ener
gy resonance states of water in its ground electronic state, (X) over tilde
= 1(1)A ', and with zero total angular momentum, is presented. The majorit
y of our calculations correspond to the even symmetry block with respect to
hydrogen atom exchange. An accurate ab initio based potential surface is e
mployed. The Lanczos method, applied to a large grid representation of the
Hamiltonian, is shown to be a straightforward method for obtaining the boun
d state energy levels. Selected eigenfunctions are also determined and seve
ral of those near the dissociation threshold are quite extended. Resonance
states just above the dissociation threshold are characterized with the aid
of damped Chebyshev iterations. Among the resonances observed are those wi
th hyperspherical and local mode character.